Alzner, 31, played four games for the Canadiens this season, posting a minus-one rating with zero points and four shots.
No specifics regarding Alzner’s decision were immediately available.
After not missing an NHL game for eight consecutive seasons, Alzner has played only 13 games in the past two years. The fifth overall pick in 2007 has seven years of playoff experience, all with the Washington Capitals.
The NHL’s Phase 3 begins Monday, as teams open training camps in their home cities.
Montreal, the No. 12 seed in the East, is scheduled to face the No. 5 Pittsburgh Penguins on Aug. 1 in Toronto to begin a best-of-five play-in series.